Radiation from an Arbitrary Source: Spinning, Charged Ring

A circular ring of radius b carries a linear charge distribution as given by Equation (6). When the ring spins about its circular symmetry axis, what power does it radiate as electromagnetic radiation? Figure 1



QUESTIONS

(Score is number right minus number wrong.)

The fields in Equation (3) are a good approximation for radiation from an arbitrary time-varying source if field point and source points satisfy
Equation (7a).
Equation (7b).
Equation (7c).
All of the above.
The fields in Equation (3) are not accurate for purposes other than estimating radiation because, in more accurate expressions for the fields, terms that fall off faster than 1/r have been arbitrarily discarded.
True
False
Time dependent factors in the expressions for fields in Equation (3) must be evaluated at
present time, Equation (8a).
a representative retarded time, Equation (8b).
strict retarded time, Equation (8c).
The electric and magnetic fields in Equation (3) are
parallel to one another.
perpendicular to one another.
The vectors shown as Equation (9a) and (9b) must be perpendicular to one another for the Poynting vector to be nonzero.
True
False
The Poynting vector for the fields of Equation (3) is directed
inward along (Equation (9a)).
inward along (Equation (9b)).
outward along (Equation (9a)).
outward along (Equation (9b)).
perpendicular to (Equation (9a) and (9b)).
The Poynting vector for these fields is the power radiated by the source.
True
False
To obtain the power being radiated we must integrate the Poynting vector over a sphere at a distance
close to
at great distance from
at intermediate distance from
at a distance that doesn't matter relative to
the boundary of the source charges.

If the z-axis of a spherical coordinate system is oriented along the vector of Equation (9b), the fields of Equation (3) are given as Equation (10).
True
False
The power radiated by the fields of Equation (3) is given by
Equation (11a)
Equation (11b)
Neither
For a stationary (not spinning) ring of charge distributed according to Equation (12), the apparent direction of the dipole moment from is likely along
Equation (13a)
Equation (13b)
Equation (13c)
To calculate the dipole moment of the stationary ring, we should substitute according to Equation (14) into Equation (4).
True
False
To obtain the expression of Equation (9b) for use in calculating the power radiated by a ring that spins counterclockwise (as seen from above), we should modify the expression for a stationary ring by using
Equation (15a)
Equation (15b)
Equation (15c)
Equation (15d)
The radiated power for the spinning ring is given by Equation (16).
True
False
EQUATIONS

Equations


Equations


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